We analyze the effects of irreversible chemical reactions of the first and higher orders and aqueous-phase dissociation reactions on the rate of trace gas scavenging by rain in the atmosphere with non-uniform concentration and temperature. We employ an one-dimensional model of precipitation scavenging of chemically active soluble gaseous pollutants that is valid for small gradients of temperature and concentration in the atmosphere. It is demonstrated that transient altitudinal distribution of concentration under the influence of rain is determined by the partial hyperbolic differential equation of the first order. Scavenging coefficients are calculated for wet removal of chlorine, nitrogen dioxide and sulfur dioxide for the exponential and linear initial altitudinal distributions of trace gases concentration in the atmosphere and linear and uniform altitudinal temperature distributions. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for sulfur dioxide are in a good agreement with the available atmospheric measurements.